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Popular Calculus >

integral from 0 to 2 of x^2-x

Solution

\int_{0}^{2} x^{2} - x d x

Solution

\frac{2}{3}

+1

Decimal

0.66666 \dots

Solution steps

\int_{0}^{2} x^{2} - x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{2} x^{2} d x - \int_{0}^{2} x d x

\int_{0}^{2} x^{2} d x = \frac{8}{3}

\int_{0}^{2} x d x = 2

= \frac{8}{3} - 2

Simplify

\frac{8}{3} - 2 : \frac{2}{3}

= \frac{2}{3}

Graph

Popular Examples

integral from-2 to-1 of 1/(xsqrt(x^2-1))

\int_{- 2}^{- 1} \frac{1}{x x ^{2} - 1} d x

integral from-1 to 1 of t^2

\int_{- 1}^{1} t^{2} d t

integral from 0 to 1 of ax+bx^2

\int_{0}^{1} a x + b x^{2} d x

integral from-1 to 1 of-sqrt(1-x^2)

\int_{- 1}^{1} - 1 - x^{2} d x

integral from 0 to 4 of x^2e^{x^3}

\int_{0}^{4} x^{2} e^{x^{3}} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of x^2-x ?
The integral from 0 to 2 of x^2-x is 2/3